Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finely resolved. A strategy to reduce such computational costs is dynamical low-rank approximation (DLRA), which represents and evolves the solution on a low-rank manifold, thereby significantly decreasing computational and memory requirements. Efficient discretizations for the DLRA evolution equations need to be carefully constructed to guarantee stability while enabling mass conservation. In this work, we focus on the Su-Olson closure leading to a linearized internal energy model and derive a stable discretization through an implicit coupling of internal energy and particle density. Moreover, we propose a rank-adaptive strategy to preserve local mass conservation. Numerical results are presented which showcase the accuracy and efficiency of the proposed low-rank method compared to the solution of the full system.

翻译：热辐射传输问题的计算方法在空间和方向域精细离散时，会面临高昂的计算成本和巨大的内存占用。降低此类计算成本的一种策略是动态低秩近似（DLRA），该方法在低秩流形上表示和演化解，从而显著降低计算和内存需求。需要精心构建DLRA演化方程的高效离散格式，以在保证稳定性的同时实现质量守恒。本文聚焦于Su-Olson闭包导出的线性化内能模型，通过内能与粒子密度的隐式耦合推导出稳定的离散格式。此外，我们提出一种秩自适应策略以保持局部质量守恒。数值结果展示了所提低秩方法与全系统求解相比的精度和效率。